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Matrix
All Questions (Page: 1)
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All Questions (PDF)
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Study Material (PDF)
All Questions (PDF)
English Version
Self Assesment
Sort As
Serial Number
Newly Added
Language
English
Click on each question to see answer & solution.
Question No: #1
If $ A = \begin{pmatrix} 0 & 2b & c \\ a & b & -c \\ a & -b & c \end{pmatrix} $ and `A^TA=I`, then find the value of `a, b, c`
Ans: `a = \pm \frac{1}{\sqrt{2}}, b = \pm \frac{1}{\sqrt{6}}, c = \pm \frac{1}{\sqrt{3}}`
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Question No: #2
If $ A = \begin{pmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{pmatrix} $ is a singular matrix, then value of `x` is -- (a) `0`, (b) `1`, (c) `3`, (d) `-3`
Ans: (d) `-3`
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Question No: #3
If $ A = \begin{bmatrix} 2 & -1 \\ -4 & 3 \end{bmatrix} $, then justify the following relation: `(A^2)^{-1} = (A^{-1})^2`
Ans:
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Question No: #4
If `A` is a skew-symmetric matrix and `I+A` isa non-singular matrix, then show that `(I-A)(I+A)^{-1}` is an orthogonal matrix.
Ans:
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Question No: #5
If $ A = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} $, then `A^5` is -- (a) `5A`, (b) `10A`, (c) `16A`, (d) `32A`
Ans: (c) `16A`
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Question No: #6
Show that the matrix $ \begin{bmatrix} 1 & 1 & 3 \\ 5 & 2 & 6 \\ -2 & -1 & -3 \end{bmatrix} $ is a Nilpotent matrix of index 3.
Ans: N.A.
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Question No: #7
If `A` is a skew symmetric matrix, then show that `A^2` is a symmetric matrix.
Ans:
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Question No: #8
If $ A = \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix} $ and `a`, `b` are two real numbers such that `A^2+aA+bI=O` (where `I` & `O` are unit & zero matrix), then find `A^{-1}`
Ans: $ A^{-1} = \begin{bmatrix} 7 & 2 \\ 1 & 5 \end{bmatrix} $
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Question No: #9
If $ A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} $ and $ B = \begin{bmatrix} 2 & 1 \\ 1 & 0 \end{bmatrix} $, then show that `(A+B)^2 \ne A^2+2AB+B^2`
Ans:
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Question No: #10
Find a matrix `A` such that $ A \begin{bmatrix} 4 & -2 \\ 0 & 5 \end{bmatrix} + \begin{bmatrix} -1 & 3 \\ -9 & 6 \end{bmatrix} = \begin{bmatrix} 3 & 16 \\ 7 & 8 \end{bmatrix} $
Ans:
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